Beasley was married to Christopher Sansocie from 1970 until their divorce in 1972. From 1985 until their divorce in 1988, she was married to actor Vincent Schiavelli (who died in 2005); they had one son, Andrea Schiavelli. In 1999, Beasley married for the third time to her current husband Jim Bosche.
Beasley has also worked as a voice Actress. She is probably best known for Miss Alordayne Grotke in the popular Walt Disney TV series Recess and in 1999 she appeared in the movie Stuart Little along with her co star from Recess, Dabney Coleman.
She also narrated for Playhouse Disney from 2000 until 2007.
During the summer of 2009, she was seen onstage in The Drowsy Chaperone at Gateway Playhouse on Long Island, playing Mrs. Tottendale.
She replaced Veanne Cox in the role of Mme. Renaud/Mme. Dindon in the Tony Award-winning revival of La Cage aux Folles alongside Kelsey Grammer and Douglas Hodge on September 14, 2010.
In the Spring of 2014, she portrayed Doris in the musical Damn Yankees with Lora Lee Gayer at the Goodspeed Opera House in East Haddam, Connecticut.
